The Cairo Geniza is surely the most important manuscript source for the study of Judaeo-Arabic texts, that is to say, texts whose language is Arabic written in Hebrew characters. This paper is an overall survey of the Judaeo-Arabic material in the 54 Arabic boxes of the Old Series in the Taylor-Schechter Genizah Collection. This collection which is housed in the Cambridge University Library is the largest collection of Geniza pieces to be found in any one place, with some 140,000 fragments. The Judaeo-Arabic material we are specifically dealing with here comprises some 7,000 manuscript fragments, research on which is now being prepared for publication. The discussion is limited to present research; it does not include references to other oriental collections such as the Firkovitch in St. Petersburg, which comprises not only fragments but codices (some almost complete) and a much wider range of Karaite Arabic material. As the Firkovitch collection is at last becoming more accessible, its contents will obviously need to be studied at a later stage in relation to the Cambridge Geniza material.